In quantum electrodynamics, the vertex function describes the coupling between a photon and an electron beyond the leading order of perturbation theory. In particular, it is the one particle irreducible correlation function involving the fermion , the antifermion , and the vector potential A.
The vertex function can be defined in terms of a functional derivative of the effective action S<sub>eff</sub> as
The dominant (and classical) contribution to is the gamma matrix , which explains the choice of the letter. The vertex function is constrained by the symmetries of quantum electrodynamics â Lorentz invariance; gauge invariance or the transversality of the photon, as expressed by the Ward identity; and invariance under parity â to take the following form:
where , is the incoming four-momentum of the external photon (on the right-hand side of the figure), and and are the Dirac and Pauli form factors, respectively, that depend only on the momentum transfer q<sup>2</sup>. At tree level (or leading order), and . Beyond leading order, the corrections to are exactly canceled by the field strength renormalization. The form factor corresponds to the anomalous magnetic moment a of the fermion, defined in terms of the Landé g-factor as:
In 1948, Julian Schwinger calculated the first correction to anomalous magnetic moment, given by <blockquote></blockquote>where ñ is the fine-structure constant.